Hi, can someone please help me show that the MC is aperiodic?

$\displaystyle X_t = \phi X_{t-1} + \epsilon_t, X_0 = 0$ and $\displaystyle |\phi|<1$,

where $\displaystyle \epsilon_1,\epsilon_2, \cdots $ are all independent N(0,1).

like i know if $\displaystyle X_t$ can reach any subspace in one step then it is aperiodic, but Im very unsure on how i go about showing this..

can someone please help me? or just guide me?